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Register a new userOn classification of conformal vectors in vertex operator algebra and the vertex algebra automorphism group
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Authors
Yuto Moriwaki
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Herein we study conformal vectors of a Z-graded vertex algebra of (strong) CFT type. We prove that the full vertex algebra automorphism group transitively acts on the set of the conformal vectors of strong CFT type if the vertex algebra is simple. The statement is equivalent to the uniqueness of self-dual vertex operator algebra structures of a simple vertex algebra. As an application, we show that the full vertex algebra automorphism group of a simple vertex operator algebra of strong CFT type uniquely decomposes into the product of certain two subgroups and the vertex operator algebra automorphism group. Furthermore, we prove that the full vertex algebra automorphism group of the moonshine module over the field of real numbers is the Monster.
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We first determine the automorphism group of the twisted Heisenberg-Virasoro vertex operator algebra $V_{mathcal{L}}(ell_{123},0)$.Then, for any integer $t>1$, we introduce a new Lie algebra $mathcal{L}_{t}$, and show that $sigma_{t}$-twisted $V_{mathcal{L}}(ell_{123},0)$($ell_{2}=0$)-modules are in one-to-one correspondence with restricted $mathcal{L}_{t}$-modules of level $ell_{13}$, where $sigma_{t}$ is an order $t$ automorphism of $V_{mathcal{L}}(ell_{123},0)$. At the end, we give a complete list of irreducible $sigma_{t}$-twisted $V_{mathcal{L}}(ell_{123},0)$($ell_{2}=0$)-modules.
For a C1-cofinite vertex algebra V, we give an efficient way to calculate Zhus algebra A(V) of V with respect to its C1-generators and relations. We use two examples to explain how this method works.
In this paper the W-algebra W(2,2) and its representation theory are studied. It is proved that a simple vertex operator algebra generated by two weight 2 vectors is either a vertex operator algebra associated to a highest irreducible W(2,2)-module or a tensor product of two irreducible Virasoro vertex operator algebras. Furthermore, any rational, C_2-cofinite simple vertex operator algebra whose weight 1 subspace is zero and weight 2 subspace is 2-dimensional, and with central charge c=1 is isomorphic to L(1/2,0)otimes L(1/2,0).
In this paper, we study a certain deformation $D$ of the Virasoro algebra that was introduced and called $q$-Virasoro algebra by Nigro,in the context of vertex algebras. Among the main results, we prove that for any complex number $ell$, the category of restricted $D$-modules of level $ell$ is canonically isomorphic to the category of quasi modules for a certain vertex algebra of affine type. We also prove that the category of restricted $D$-modules of level $ell$ is canonically isomorphic to the category of $mathbb{Z}$-equivariant $phi$-coordinated quasi modules for the same vertex algebra. In the process, we introduce and employ a certain infinite dimensional Lie algebra which is defined in terms of generators and relations and then identified explicitly with a subalgebra of $mathfrak{gl}_{infty}$.
It is shown that any simple, rational and C_2-cofinite vertex operator algebra whose weight 1 subspace is zero, the dimension of weight 2 subspace is greater than or equal to 2 and with central charge c=1, is isomorphic to L(1/2,0)otimes L(1/2,0).
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